Riemannian Submanifolds

  • Sylvestre Gallot
  • Dominique Hulin
  • Jacques Lafontaine
Part of the Universitext book series (UTX)


Let (M~,〈,〉) be a Riemannian manifold, and (M,g) be a Riemannian submanifold of M~. We want to compute the curvature of M in terms of the curvature of M~. We first consider the case where M is an hypersurface of M~ (the reader can keep in mind the example of surfaces in R3). The general case is treated in exercise.


Vector Field Riemannian Manifold Orthonormal Basis Sectional Curvature Fundamental Form 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Sylvestre Gallot
    • 1
  • Dominique Hulin
    • 2
  • Jacques Lafontaine
    • 3
  1. 1.Université de SavoieChambéry CedexFrance
  2. 2.Centre d’Orsay, MathématiqueUniversité Paris11Orsay CedexFrance
  3. 3.U.F.R. de MathématiquesUniversité Paris 7Paris Cedex 05France

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